Data for the Boeing 747-100

The Boeing 747 is a highly successful, large, four-engined turbofan transport aircraft. The model 100 first entered service in January 1970, and since then it has continued to be developed through a series of models and special versions. As of May 1990, only versions of the model 400 were being marketed. By the year 1994, close to 800 Boeing 747s were in operation around the world, and the aircraft was still in produc­tion.

The data for the Boeing 747-100 contained in this appendix are based on Heffley and Jewell (1972). A three-view drawing of the aircraft is given in Fig. E. l. A body axis system FB is located with origin at the CG and its x-axis along the fuselage refer­ence line (FRL). The CG is located at 0.25 c (i. e., h = 0.25), and this is the location that applies for the tabulated data. The thrust line (TL) makes an angle of 2.5° with respect to the FRL as shown.

Three flight cases are documented in the data tables. They all represent straight and level steady-state flight at a fixed altitude. Case I has the aircraft in its landing configuration with 30° flaps, landing gear down, and an airspeed 20% above the stalling speed. Cases II and III represent two cruising states with the flaps retracted and the gear up.

The data in Table E. l define the flight conditions that apply to the three cases. It should be noted that the moments and product of inertia are given relative to the body frame FB shown in Fig. E. l. Flere the weight and inertias for Case I are smaller than those for the other two cases because the amount of fuel on board during landing is less than that during the cruise. If the data are to be applied to a reference frame dif­ferent from FB (e. g., to stability axes Fs) then the given inertias will have to be trans­formed according to (B.12,3). Note that FB can be rotated into Fs by a single rotation of f about the у-axis. Values for f are contained in Table E. 1.

The dimensional derivatives corresponding to FB of Fig. E. 1 are contained in Ta­bles E.2 to E.4. Since FB can be rotated into the stability axes Fs by a single rotation of £ about the у-axis, it follows that the transformations of (B. 12,6 and B. 12,7) can be used to obtain the derivatives corresponding to Fs. Values for £ are contained in Table E. l.

Table E. l

Boeing 747-100 Data

(S = 5,500 ft2, b = 195.68 ft, c = 27.31 ft, h = 0.25) Case I Case II Case III Altitude (ft) 0 20,000 40,000 M 0.2 0.5 0.9 V (ft/s) 221 518 871 W(lb) 5.640 X 105 6.366 X 105 6.366 X 105 Ix (slug-ft2) 1.42 X 107 1.82 X 107 1.82 X 107 /,, (slug-ft2) 3.23 X 107 3.31 X 107 3.31 X 107 h (slug-ft2) 4.54 X 107 4.97 X 107 4.97 X 107 (Slug-ft2) 8.70 X 105 9.70 X 105 9.70 X 105 £ (degrees) -8.5 -6.8 -2.4 CD 0.263 0.040 0.043

Table E.2

Boeing 747-100 Dimensional Derivatives

Case I (M = 0.2) Longitudinal X(lb) Z(lb) M(fflb) и (ft/s) -3.661 x 102 -3.538 X 103 3.779 X 103 w (ft/s) 2.137 X 103 -8.969 X 103 -5.717 X 104 q (rad/s) 0 -1.090 X 105 -1.153 X 107 w (ft/s2) 0 5.851 X 102 -7.946 X 103 8,(rad) 1.680 X 104 -1.125 X 105 -1.221 X 107

Lateral У (lb) L(ft-lb) N(fflb) v (ft/s) -1.559 X 103 -8.612 X 104 3.975 X 104 p (rad/s) 0 -1.370 X 107 -6.688 X 106 r (rad/s) 0 4.832 X 106 -1.014 X 107 8a (rad) 0 -3.200 X 106 -1.001 X 106 8r(rad) 5.729 X 104 1.034 X 106 -6.911 X 106

Table E.3

Boeing 747-100 Dimensional Derivatives

Case II (M = 0.5) Longitudinal X(lb) Z(lb) M(fflb) и (ft/s) -4.883 X 10′ -1.342 X 103 8.176 X 103 w (ft/s) 1.546 X 103 -8.561 X 103 -5.627 X 104 q (rad/s) 0 -1.263 X 105 -1.394 X 107 w (ft/s2) 0 3.104 X 102 -4.138 X 103 Se (rad) 3.994 X 104 -3.341 X 105 -3.608 X 107

Lateral У (lb) Lift-lb) N(ft-lb) v (ft/s) -1.625 X 103 -7.281 X 104 4.404 X 104 p (rad/s) 0 -1.180 X 107 -2.852 X 106 r (rad/s) 0 6.979 X 106 -7.323 X 106 Sa (rad) 0 -2.312 X 106 -7.555 X 105 Sr(rad) 1.342 X 105 3.073 X 106 -1.958 X 107

Table E.4

Boeing 747-100 Dimensional Derivatives

Case III (M = 0.9) Longitudinal X(lb) Z(lb) M(ft-lb) и (ft/s) -3.954 X 102 -8.383 X 102 -2.062 X 103 w (ft/s) 3.144 X 102 -7.928 X 103 -6.289 X 104 q (rad/s) 0 -1.327 X 105 -1.327 X 107 w (ft/s2) 0 1.214 X 102 -5.296 X 103 Se (rad) 1.544 X 104 -3.677 X 105 -4.038 X 107

Lateral У (lb) L(ft-lb) N(ft-lb) v (ft/s) -1.198 X 103 -2.866 X 104 5.688 X 104 p (rad/s) 0 -8.357 X 106 -5.864 X 105 r (rad/s) 0 5.233 X 106 -7.279 X 106 Sa (rad) 0 -3.391 X 106 4.841 X 105 S, (rad) 7.990 X 104 2.249 X 106 -2.206 X 107

[1]An excellent account of the early history is given in the 1970 von Karman Lecture by Perkins (1970).

[2]It is also possible to speak of the stability of a transient with prescribed initial condition.

[3]For a more complete discussion, see AGARD (1959); Stevens and Lewis (1992).

[4]This word describes the position of movable elements of the airplane—for example, landing con­figuration means that landing flaps and undercarriage are down, climb configuration means that landing gear is up, and flaps are at take-off position, and so forth.

[5]When partial derivatives are taken in the following equations with respect to one of these variables, for example, ЭCJda, it is to be understood that all the others are held constant.

[6]The notation h„w indicates that the mean aerodynamic center of the wing is also the neutral point of the wing. Neutral point is defined in Sec. 2.3.

[7]Equivalent airspeed (EAS) is VE = vVpfpa where p0 is standard sea-level density.

[8]Note that a is still the angle of attack of the zero-lift line of the basic configuration, and that the lift with flap deflected is not zero at zero a.

[9] We may neglect as well all the derivatives of the symmetric forces and mo­ments with respect to the asymmetric motion variables.

[10] We may neglect all derivatives with respect to rates of change of motion vari­ables except for ZH, and Mlv.

[11]For two-dimensional incompressible flow, the area 5(f) diverges as t —» °°. That is, the derivative concept is definitely not applicable to that case.

[12]Exactly for supersonic wings, and approximately for subsonic wings.

[13]See bibliography.

[14]Rodden and Giesing (1970) have extended and generalized this method. In particular they give re­sults for finite wings.

[15]For the effect of the wing at low speeds, see Campbell and McKinney (1952).

[16]Exactly, in an isothermal atmosphere of uniform composition; approximately, in the real atmos­phere.

[17]The De Havilland Buffalo airplane.

[18]Program CC, see Appendix A.7.

[19]Based on the Piper Cherokee. The control derivatives were taken from McCormick (1979). We es­timated the stability derivatives. The numerical values used may not truly represent this airplane.

[20]Neglecting the fact that the pilot and indicator are not right at the CG.

[21]The term root locus is used throughout this chapter with the meaning ordinarily ascribed to it in the

control theory literature.

[23]See also Ribner and Ellis (1972).

[24]